Semi-analytical Procedure Research Articles

Dufour and Soret effects on MHD squeezed nanoliquid flow between parallel plates by differential transform method

Purpose This paper aims to examine the Dufour and Soret combined effects on the study of two-dimensional squeezed flow of copper water nanofluid between parallel plates along with applied (external) magnetic field. Impact of higher order chemical reaction is also considered. Design/methodology/approach The nonlinear partial differential equations (PDEs) are changed into system of ordinary differential equations (ODEs) by employing suitable similarity transformations. These transformed ODEs are then solved by means of a semianalytical method called differential transform method (DTM). Effects of several changing physical parameters on fluid flow, temperature and concentration have been deliberated through graphs. Findings It is observed that Dufour and Soret numbers are directly related to temperature profile and a reverse trend was observed in the concentration profile. Temperature enhancement is perceived for the enhanced Dufour number. Enhancement in Dufour number shows a direct association with Sh and Nu for all values of squeezing parameter. Practical implications The combined Dufour and Soret effects are used in separation of isotopes in mixture of gases, oil reservoirs and binary alloys solidification. The squeeze nanoliquid flow can be used in the field of composite material joining, rheological testing and welding engineering. Social implications This study is mainly useful for geosciences and chemical engineering. Originality/value The uniqueness in this research is the study of the impact of cross diffusion on chemically reacting squeezed nanoliquid flow with the chemical reaction order more than one in the presence of applied magnetic force using a semianalytical procedure, named DTM.

A new method for rapidly capturing the strength and full nonlinear response of partially interacting steel–concrete composite beams

A semi-analytical procedure is presented for predicting the complete flexural response of partially interacting steel–concrete composite beams up to failure. The governing equation of the Euler–Bernoulli beam theory is solved wherein concrete, steel and the shear connectors joining the concrete slab to the steel beam are assumed to have nonlinear stress-deformation relationships. The adopted constitutive relationship for the connectors allows for partial or full composite action. The solution is applicable to beams and one-way slabs subjected to concentrated or uniform load and/or their combination. The governing equation is numerically solved by satisfying the equilibrium and compatibility requirements along the member. For the reinforced concrete part of the composite beam, a nonlinear moment–curvature relationship is developed that accounts for concrete nonlinearity in compression and for cracking and tension-stiffening in tension as well as for steel reinforcement nonlinearity. The steel profile is assumed to have a bilinear elasto–plastic strain-hardening moment–curvature relationship. Comparison of the proposed model results with the corresponding experimental load–deflection curves and interfacial shear–slip curves of several beams tested by others shows good agreement. The relative simplicity, efficiency and easy application of the present solution make it possible to accurately predict the failure load, interfacial slip and full nonlinear response of partially interacting composite beams.

A semi-analytical procedure to determine the ion recombination correction factor in high dose-per-pulse beams.

The conventional theories and methods of determining the ion recombination correction factor, such as Boag theory and the related two voltage method and Jaffé plot extrapolation, do not seem to yield accurate results in FLASH /high dose per pulse (DPP) beams ( 10 mGy DPP). This is due to the presence of a large free electron fraction that distorts the electric field inside the chamber sensitive volume. To understand the influence of these effects on the ion recombination correction factor and to develop new expressions for it, it is necessary to re-visit the underlyingphysics. To present a mathematical procedure to develop an analytical expression for the ion recombination correction factor. The expression is the basis for an extrapolation method so the correction factor can be determined in a clinical setting. A semi-analytical solution method, the homotopy perturbation method (HPM), is used to solve the partial differential equations(PDEs) describing the charge carrier physics, including space charge and free electrons. The electron velocity and attachment rate are modeled as functions of the electric field strength. An expression for the charge collection efficiency and ion recombination correction factor are developed. A fit procedure based on this expression is used to compare it to measured data from previously published articles. Another fit procedure using a general equationis also proposed and compared to the data. The series obtained for the charge collection efficiency and the ion recombination correction factor are determined to be asymptotic series and the optimal truncation established. The ion recombination correction factor exhibits a dependency due to the free electron presence. The fit using this expression agrees well with measured data as long as (1) the DPP is below 1 Gy for chambers with a 1 mm plate separation and (2) when the DPP is below 3 Gy for chambers with a 0.5 mm plate separation. In these DPP ranges, the deviation between measured and fit value did not exceed 6%. In both chamber cases the voltage range where the fit applies decreases as DPP increases. The general equationyielded comparable results. The HPM was shown to be applicable to a complex system of PDEs and generate meaningful and novel solutions, as they include both space charge and free electrons. The HPM also lends itself to other chamber geometries. The fit procedure was also shown to yield accurate results for the ion recombination correction up to the 1 Gy DPPlevel.

An efficient and accurate semi-analytical matching technique for waveguide-fed antennas

Several RF and microwave radiating devices, such as horn antennas, Fabry–Perot cavity antennas, and aperture-fed focusing devices, are excited through rectangular waveguides. The impedance matching of the overall system (from the waveguide feed to the radiating aperture) is a task of crucial importance that is often addressed by means of brute-force parameter-sweep full-wave analyses or blind optimization algorithms. In both cases, a significant amount of memory and time resources are required. For this purpose, we propose here a simple, yet effective solution, which only requires a single full-wave simulation and a semi-analytical procedure. The former is used to retrieve the antenna input impedance at the end of the waveguide port excitation. The semi-analytical procedure consists in a transmission-line equivalent circuit that models two waveguide discontinuities (namely two capacitive irises) within the waveguide section, whose position and geometric features are finely tuned to obtain a satisfactory impedance matching around the working frequency. The proposed method is shown to be effective in diverse and attractive application-oriented contexts, from the impedance matching of a Fabry–Perot cavity antenna to that of a wireless near-field link between two aperture-fed focusing devices. A remarkable agreement between full-wave simulations and numerical results is found in all cases. Thanks to its versatility, simplicity, and a rather low demand of computational resources, the proposed approach may become an essential tool for the effective design of waveguide-fed antennas.

Experimental and numerical evaluation of hydro-thermal ageing's effects on adhesive connections in offshore structures

In offshore structures, the need to replace or strengthen existing metal components arises over time. One possible solution is the use of bonded connections. Nevertheless, the durability of the adhesive connections is highly compromised by the prolonged contact with water.In this paper, an experimental and numerical evaluation of hydro-thermal ageing's effects on polyurethane adhesive connections has been analysed. An efficient semi-analytical procedure is developed for the design or verification of existing structures reinforced by bonded steel elements. The model can evaluate the interfacial shear stress at all loading stages up to the failure of bonded joints exposed to the marine environment. The model is based on Bernoulli beam theory and satisfies the requirements of equilibrium and strain compatibility, allowing for interfacial deformations.Furthermore, the mechanical behaviour of bonded connections subject to accelerated ageing has been experimentally investigated. More in detail, an experimental program including double lap shear and end-notch flexure tests was performed to evaluate the cohesive behaviour in Mode II of a polyurethane structural adhesive under the combined effects of water and temperature during 150 days of exposure. The experimental and numerical investigation shows how the performance of the adhesive joints is influenced by the ageing conditions.

A semi-analytical matrix formalism for stress singularities in anisotropic multi-material corners with frictional boundary and interface conditions

A new general semi-analytic procedure for the characterisation of singular asymptotic elastic states in the vicinity of the apex of linearly elastic anisotropic multi-material corners, including frictional contact, is developed and tested. The corners can consist of any finite number of homogeneous wedges defined by polar sectors. The variability of configurations covered is enormous as frictional contact can be considered on one or more outer boundary surfaces or interfaces, in addition to a large variety of homogeneous boundary conditions and perfect bonding or frictionless sliding interface conditions between wedges in the corner. The Coulomb rate-independent and dry frictional contact law is assumed. One of the novelties is that, in addition to the singularity exponent λ, the angle ω of the friction tangential stress vector on each frictional contact surface is an a priory unknown to be determined by solving a nonlinear corner eigensystem. The procedure, which considers power-law stress singularities, is based on the Stroh formalism of anisotropic elasticity, assuming generalised plane strain (2.5D) conditions, and on the semi-analytic matrix formalism for wedge transfer-matrices and boundary and interface condition matrices. This makes it, firstly, very suitable for computational implementations, secondly, very efficient especially in cases with several perfectly bonded homogeneous wedges, and, thirdly, very accurate due to its fully semi-analytic nature. The code developed is tested by solving a large variety of examples, comparing the present results with those obtained by solving closed-form corner-eigenequations deduced by previous authors for specific useful practical configurations, confirming the extremely high accuracy of the present code in the computation of λ and ω. The differences observed in some cases with anisotropic materials are explained by the fact that some of the previous authors did not take the true 3D Coulomb friction law into account.

Load Bearing Capacity of Lateral Loaded Piles in Watered Carpathian Flysch

In this paper, flysch is presented as a representative material of a wide section of the Carpathian Mountains, with some areas in Poland highlighted. The geological structure of this area is complex due to the alternating layers of blocky rock masses and soil (Vessia et al., 2017). Such a complex pattern is seen in some Alpine flysch slopes, such as the Ingelsberg landslide area (Romeo et al., 2015). Many authors are monitored, predicted landslides (Allasia et al., 2013; Bertacchini et al., 2009; Casagli et al., 2010) by sophisticated sensors. The rock-soil flysch successions have become intensively fissured as a result of their geological history, weathering (precipitation and snowmelt), and long-term water retention, especially on the surface layers. These complex materials are characterised by heterogeneous lithologies, whose mechanical properties are largely uncertain. These geological structures have also been confirmed by monitoring and control studies performed on a large number of landslides (Bednarczyk, 2014). One of the most striking phenomena is the sudden decrease in the strength parameters in the studied rocks in the direction parallel to the layers due to watering. The process is made possible by heterogeneous fractured strong rock layers with high permeability coefficients for water. This study precisely describes the phenomena occurring at the contact area between the component layers of flysch under the wet conditions of a weak plane. An elastic-plastic analysis method that considers the developed strength model at the surfaces of the contact areas (Biernatowski & Pula, 1988; Pula, 1997) has been used to estimate the load capacity for piles working under a horizontal load. The piles are part of a reliability chain (Pula, 1997) in a given construction and are the first element of concern for monitoring (Muszynski & Rybak, 2017). A particular device intended to study the dependence of the shear stress on a fixed failure surface in a controlled consolidation condition was utilized. The study was conducted for a wide range of displacements and for different values of stabilized vertical stresses of consolidation. The complexity of the processes occurring in the shear zone, presented as a detailed study of the material crack mechanics, is highlighted. The laboratory results were used to construct the mechanical model of the slip surface between the soil and rock with the description supported by a neural network (NN) approximation. The artificial NN was created as a multi-layered, easy to use approach for interpreting results and for quick reconstruction of approximated values useful for the calculations presented in laterally loaded piles. For the calculations, long, sheared strips of material were considered in a semi-analytical procedure to solve a differential equation of stability. The calculations are intended to reveal the safety indexes for a wide range of boundary tasks as the most significant indicator for design decisions.

Flügge shell theory and solution for the vibration analysis of a thin elastic cylindrical panel of varying curvature

In this paper, the free vibration behavior of isotropic and orthotropic cylindrical shell panels with variable curvature subjected to certain ends boundary conditions is analyzed by the transfer matrix technique and solved by the Romberg integration approach. Flügge’s shell theory is employed to model the governing three-dimensional equations of vibration and Fourier’s approach is used to deform the displacement fields as trigonometric functions in the longitudinal direction. As a result of a semi-analytical procedure is conducted, the coupled governing equations of panel problem can be written in a matrix partial differential equation of first order with variable coefficients and reduced from the two-dimensional problem to one-dimensional one which is solved numerically as an initial-value problem. The proposed model is applied to get the natural frequencies and mode shapes for the vibration behavior of two-side simply-supported cylindrical panels with simply-supported, free-free, clamped-free and clamped-clamped ends boundary conditions lying at their curved edges. The sensitivity of the vibration behavior to the variety of curvature, panel parameters and material orthotropy of shell is studied.

Investigation of the initial residual stress effects on a work roll maximum in-service stress in hot rolling process by a semi-analytical method

A High magnitude of von Mises stress is considered a source of plastic deformation, fatigue crack initiation, and surface defects. A Detailed finite element model (FEM) was proposed here to estimate the thermo-mechanical stress and residual stress components at an industrial hot rolling work roll during the rolling process. Also, a semi-analytical procedure was developed here to study the effect of the initial residual stress components that remained after the work roll heat treatment process on maximum von Mises stress. The work roll referred to here was an Indefinite Chilled Double Poured (ICDP) cast iron roll that was used as the fifth finishing stand of strips hot rolling. Residual stress components were measured by the ring-core method at two stages, after the heat treatment process as initial components and after the service life of the work roll as final components. Estimated residual stress components by the developed method were compared with final experimental residual stress measurements to verify the FEM. Finally, by using artificial neural network and genetic algorithm, the maximum value of von Mises stress was predicted, and initial residual stress components were optimized in order to minimize the maximum value of attained von Mises stress at the work roll surface, where the most fatigue cracks initiate and grow.

A mathematical study of water wave interaction with a thin perforated barrier in a two-layer fluid over a permeable bottom

This article studies the impact of a submerged interface-piercing perforated barrier in a two-layer fluid flowing over a permeable bottom. We investigate oblique wave scattering, trapping and radiation due to the structure focusing on the bottom permeability. The dead water phenomenon is analysed with the consideration of the bottom permeability, which results in a higher variation of the interfacial wave due to the bottom permeability. The matched eigenfunction expansion method and the least square technique are used to calculate various hydrodynamic coefficients. Wave energy identity relation is derived for the scattering scenario, and the associated energy loss due to the barrier is calculated. In order to attain the maximum wave dissipation, an ideal porous-effect parameter of the barrier is proposed for consideration, and it is observed that larger values of porous-effect parameter result in the lowest feasible pressure distribution. A good comparison with a prior result justifies the current semi-analytical procedure. Furthermore, the verification of the energy-identity terms aid in the validation of the computed results. Additionally, wave trapping in a confined region is examined by investigating reflection coefficients by considering a rigid wall. The thin perforated barrier model is further considered for examining the radiation aspect while considering its slow motion. For various porous-effect parameters of the barrier, the amplitude ratio of the radiated potential is investigated, and it is clearly observed that higher frequency significantly lowers the amplitude for both free surface and interfacial propagating modes. The impact of the perforated barrier is analysed by investigating the essential hydrodynamic coefficients, namely, added mass and damping coefficient.

Coupled Chemo-Mechanical Swelling Behavior of PH-Sensitive Hollow Cylinder Hydrogels under Extension–Torsion and Internal Pressure: Analytical and 3D FEM Solutions

The coupled transient chemo-mechanical behavior as well as the large deformation behavior under various complex load conditions must be taken into account when designing a functional responsive polymer actuator or sensor. One sort of deformation that can be used to characterize the properties of materials with complicated behavior, like soft hydrogels, is coupled extension and torsion with internal pressure. It is important to thoroughly research the complex kinetics of pH-hydrogels with coupled diffusion and massive deformation behavior. The transient behavior of cylindrical hydrogels under coupled extension–torsion with internal pressure under indifferent conditions is proposed in this work using a reliable semi-analytical method. In this regard, an analytical solution is offered to inspect this problem, which is used as a common experimental methodology for the characterization and modeling of polymeric materials. The results show that the rate of deformation and the physical characteristics of the material have a substantial impact on the cylindrical hydrogel’s transient behavior under coupled extension–torsion and internal pressure. For the same problem, a 3D finite element study was done to assess the analytical solution. The accuracy of our method is supported by the results’ agreement in both the FE analysis and the proposed approach. However, offering such a solution for this complex problem is of tremendous relevance given the significantly cheaper computational cost of analytical methods when compared to FEM. Additionally, the calculations indicate a complex reaction force and moment because the hydrogel experiences nonlinear Poynting-type effects in this deformation domain. The suggested semi-analytical procedure’s resilience behavior is demonstrated by the visualization of the effects of various material properties. This method can be used to calibrate constitutive models and to develop and improve hydrogel structures.

A semi-analytic study of self-interacting dark-matter haloes with baryons

ABSTRACT We combine the isothermal Jeans model and the model of adiabatic halo contraction into a semi-analytic procedure for computing the density profile of self-interacting dark-matter (SIDM) haloes with the gravitational influence from the inhabitant galaxies. The model agrees well with cosmological SIDM simulations over the entire core-forming stage up to the onset of gravothermal core-collapse. Using this model, we show that the halo response to baryons is more diverse in SIDM than in CDM and depends sensitively on galaxy size, a desirable feature in the context of the structural diversity of bright dwarfs. The fast speed of the method facilitates analyses that would be challenging for numerical simulations – notably, we quantify the SIDM halo response as functions of the baryonic properties, on a fine mesh grid spanned by the baryon-to-total-mass ratio, Mb/Mvir, and galaxy compactness, r1/2/Rvir; we show with high statistical precision that for typical Milky-Way-like systems, the SIDM profiles are similar to their CDM counterparts; and we delineate the regime of core-collapse in the Mb/Mvir − r1/2/Rvir space, for a given cross section and concentration. Finally, we compare the isothermal Jeans model with the more sophisticated gravothermal fluid model, and show that the former yields faster core formation and agrees better with cosmological simulations. We attribute the difference to whether the target CDM halo is used as a boundary condition or as the initial condition for the gravothermal evolution, and thus comment on possible improvements of the fluid model. We have made our model publicly available at https://github.com/JiangFangzhou/SIDM.

Fault friction under thermal pressurization during large seismic-slip: Numerical analyses and extension of the model of frictional slip

Earthquake faults are the result of severe strain localization in rocks deep down in the earth’s crust. This localized deformation is controlled by the size of the microstructure and various Thermo-Hydro-Mechanical (THM) couplings, whose modeling is central for understanding earthquake nucleation and seismic energy release. We model this challenging system using the Cosserat theory and by considering large shear deformations during seismic slip. Our numerical results justify the rate and state friction law (Dieterich, 1992; Ruina, 1983a), which describes empirically the fault tribology. This shows the importance of the underlying physics of our model for fault friction. In our analyses traveling shear bands along the thickness of the fault are present, leading to oscillations in the fault’s frictional response. Existing numerical analyses presented in Rattez et al. (2018a, 2018b, 2018c) do not capture this behavior, which goes beyond the established models of uniform shear (Lachenbruch, 1980) and shear on a mathematical plane (Rice, 2006a). Recent experimental results, that insulate thermal pressurization from other weakening mechanisms (Badt et al., 2020), corroborate our numerical results. Our results motivate us to extend the classical model of thermal pressurization in Mase & Smith (1987) and Rice (2006b) to incorporate different strain localization modes, temperature and pore fluid pressure boundary conditions.In particular, we start our analysis by using the normalized coupled system of partial differential equations that include the THM couplings for the case of a Cosserat continuum. We then perform a bifurcation analysis, which indicates that traveling shear bands are possible inside the fault gouge. Next, we derive our non linear mesh independent numerical results accounting for the influence of large displacements by using and Adaptive Lagrangian Eulerian (ALE) procedure. We introduce viscosity in our numerical analyses for the rate and state phenomenology to emerge. We corroborate our numerical results comparing them to similar laboratory experiments. Furthermore, we modify the Volterra integral equation of the classical model of thermal pressurization in Mase & Smith (1987) and Rice (2006b), which we solve by a semi analytical procedure, in order to capture the effect of isothermal drained boundary conditions and traveling shear bands. Our results reappraise and extend the established models of frictional weakening due to thermal pressurization during coseismic slip.

Metagrating-Assisted High-Directivity Sparse Regular Antenna Arrays for Scanning Applications

We present an analytical scheme for designing metagrating-enhanced sparse antenna arrays. Unlike previous work, the proposed method does not involve time-consuming cost function optimizations, complex structural manipulations on the active array or demanding computational capabilities. Instead, it merely requires the integration of a passive metagrating (MG) superstrate, a planar periodic arrangement of subwavelength capacitively-loaded wires (meta-atoms), synthesized conveniently via a semianalytical procedure to guarantee suppression of grating lobes in the sparse configuration. Correspondingly, we extend previous formulations to enable excitation of the MG by the active array elements, deriving analytical relations connecting the passive and active element distribution and electrical properties with the scattered fields, eventually allowing resolution of the detailed device configuration leading to optimal directivity. Importantly, considering typical active array applications, the semianalytical synthesis scheme is further developed to take full advantage of the various degrees of freedom in the system, harnessing them to support scanning in a wide range of extreme angles while maintaining a single directive beam. The resultant methodology, verified in simulations to work well also for large finite arrays, offers an original path for mitigating grating lobes in sparse arrays with scanning capabilities, yielding a complete printed-circuit-board compatible design without relying on full-wave optimization.

Supratransmission in a vibro-impact chain

The paper addresses the supratransmission (ST), i.e., emergence of the propagating waves in a nonlinear chain forced in the attenuation zone of the linear substructure. In the considered model, the nonlinearity is realized through impacts of particles in a linear chain with on-site constraints. This special form of the nonlinearity allows deriving the exact solutions for edge states of the semi-infinite boundary-driven chain. Stability of these edge states is assessed through semi-analytic procedure for direct evaluation of the monodromy matrix. The ST appears when the instability of the localized edge states leads to solutions with frequency components belonging to the propagation zone of the linear substructure. This mechanism substantially differs from previously observed ST scenarios, related to a generation of the propagating breathers. Various bifurcation sequences eventually leading to the ST are revealed and discussed.

Evaluation of input geological parameters and tunnel strain for strain-softening rock mass based on GSI

The regression analysis method is being widely adopted to analyse the tunnel strain, most of which ignore the strain-softening effect of the rock mass and fail to consider the influence of support pressure, initial stress state, and rock mass strength classification in one fitting equation. This study aims to overcome these deficiencies with a regression model used to estimate the tunnel strain. A group of geological strength indexes (GSI) are configured to quantify the input strength parameters and deformation moduli for the rock mass with a quality ranging from poor to excellent. A specific semi-analytical procedure is developed to calculate the tunnel strain around a circular opening, which is validated by comparison with those using existing methods. A nonlinear regression model is then established to analyse the obtained tunnel strain, combining twelve fitting equations to relate the tunnel strain and the factors including the support pressure, GSI, initial stress state, and critical softening parameter. Particularly, three equations are for the estimation of the critical tunnel strain, critical support pressure, and tunnel strain under elastic behaviour, respectively; and the other nine equations are for the tunnel strain with different strain-softening behaviours. The relative significance between the GSI, the initial stress and the support pressure on the tunnel strain is assessed.

On a Novel Algorithmic Determination of Acoustic Low Frequency Coefficients for Arbitrary Impenetrable Scatterers

The calculation of low frequency expansions for acoustic wave scattering has been under thorough investigation for many decades due to their utility in technological applications. In the present work, we revisit the acoustic Low Frequency Scattering theory, and we provide the theoretical framework of a new algorithmic procedure for deriving the scattering coefficients of the total pressure field, produced by a plane wave excitation of an arbitrary, convex impenetrable scatterer. The proposed semi-analytical procedure reduces the demands for computation time and errors significantly since it includes mainly algebraic and linear integral operators. Based on the Atkinson–Wilcox theorem, any order low frequency scattering coefficient can be calculated, in finite steps, through algebraic operators at all steps, except for the last one, where a regular Fredholm integral equation with a continuous and separable integral kernel is needed to be solved. Explicit, ready to use formulae are provided for the first three low frequency scattering coefficients, demonstrating the applicability of the algorithm. The validation of the obtained formulae is demonstrated through recovering of the well-known analytical results for the case of a radially symmetric scatterer.

Hybrid semi-analytical calculation of the stress intensity factor for heterogeneous and functionally graded plates

One of the significant successes in the Linear Elastic Fracture Mechanics field is the groundwork of stress intensity factor computation. By considering a linear elastic model of 2-D and 3-D finite width rectangular plates, the present work shows a new semi-analytical procedure to compute the stress intensity factor of the crack opening mode. Plates are made of homogeneous and graded heterogeneous media, characterized by different crack lengths and elastic moduli. The stress intensity factor was evaluated using the proposed procedure combined with a numerical one without the knowledge of the material properties in the crack tip to overcome the limitations related to the errors affecting the traditional solutions in the case of spatial variation of the constitutive properties within the structure. The obtained results have been compared with the well-established theoretical literature for homogeneous cases. Moreover, a mesh sensitivity analysis has been performed by varying the elements’ number along the crack length showing the effectiveness and feasibility of the proposed procedure, even in the case of coarse discretization, with consistent advantage in terms of computational costs. Furthermore, by keeping the crack length constant, parametric analyses have been carried out to investigate the effects of material graded heterogeneities on the stress distribution. The limitation of this study concerns the assumption that the delamination front is supposed to be straight, and the proposed strategy cannot be implemented in the case of an arbitrarily shaped front. Finally, the application of this research is in the field of production engineering and, Without setting a priori-specific discretization of the domain near the tip, the present approach paves the way to further implementation in crack propagation procedures.

Semi-analytical solving procedure for the dynamics of charged particle in parametrically variable magnetic field

Semi-analytical solving procedure for the dynamics of charged particle in parametrically variable magnetic field

Incompressible energy spectrum from wave turbulence

Bose–Einstein condensates with their superfluidity property provide an interesting parallel to classical fluids. Due to the Kolmogorov spectrum of homogeneous turbulence the statistics of the incompressible velocity field is of great interest, but in superfluids obtaining quantities such as the statistics of the velocity field from the macroscopic wavefunction turns out be a complicated task; therefore, most of the work up to now has been numerical in nature. We made use of the Weak Wave Turbulence (WWT) theory, which provides the statistics of the macroscopic wavefunction, to obtain the statistics of the velocity field, which allowed us to produce a semi analytical procedure for extracting the incompressible energy spectrum in the WWT regime. This is done by introducing an auxiliary wavefunction that preserves the relevant statistical and hydrodynamical properties of the condensate but with a homogeneous density thus allowing for a simpler description of the velocity field.